In the context where quantum geometry is studied for driving parameters of the Hamiltonian one tends to talk about the quantum geometric tensor (QGT) [1]}, the entries of which are the FS and which, away from level crossings, is the same object as the QFI matrix defined in Eq. REF . The form of the QFI matrix in terms of the covariance may thus be thought of as an adiabatic form of the QFI [2]}. In the vicinity of the critical point the QGT and QFI matrix display different scaling relationships  [1]}, [4]}. In this work we focus on the QFI matrix in this adiabatic form, since determining the entire spectrum is generally a very hard problem for all but a handful of exactly solvable models. If, however, the operators generating the transformations are relevant in a renormalization group sense then both the QFI and QGT will exhibit divergences at the critical point.
